1. **State the problem:** Find the measure of the inner angle formed by the hour hand and the minute hand at exactly 8:20. 2. **Formula and rules:** - The minute hand moves 6 degrees per minute: $$6 \times \text{minutes}$$. - The hour hand moves 0.5 degrees per minute plus 30 degrees per hour: $$30 \times \text{hours} + 0.5 \times \text{minutes}$$. - The angle between the two hands is the absolute difference between their positions. - The inner angle is the smaller angle between them, so if the difference is more than 180 degrees, subtract it from 360 degrees. 3. **Calculate the positions:** - Minute hand at 20 minutes: $$6 \times 20 = 120^\circ$$. - Hour hand at 8:20: $$30 \times 8 + 0.5 \times 20 = 240 + 10 = 250^\circ$$. 4. **Find the difference:** $$|250 - 120| = 130^\circ$$. 5. **Determine the inner angle:** Since 130 degrees is less than 180 degrees, the inner angle is $$130^\circ$$. **Final answer:** The inner angle formed by the hour and minute hands at 8:20 is $$130^\circ$$.